Smithsonian miscellaneous collections

J^. /i^;. SMITHSONIAN MISCELLANEOUS COLLECTIONS VOLUME. 86. (WHOLE VOLUME). SMITHSONIAN. METEOROLOGICAL TABLES [based on guyot's meteorological and physical tables]. FIFTH REVISED EDITION (Corrected to January, 1931). (Publication 3116). CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTITUTION 1931.



^. SMITHSONIAN MISCELLANEOUS COLLECTIONS. VOL.. "EVERY. MAN. IS. 86. MEMBER OF SOCIETY WHO. BY HIS OBSERVATIONS. RESEARCHES. AND EXPERIMENTS. PROCURES KNOWLEDGE FOR MEN"— SMITHSON. A VALUABLE. (Publication 3215). CITY OF WASHINGTON PUBLISHED BY THE SMITHSONIAN INSTITUTION 1933.

THE SCIENCE PKESS PRINTING COMPANY LANCASTER, PENNSYLVANIA. 349550.

^oo. L.. ADVERTISEMENT. The tions. present series, entitled " Smithsonian Miscellaneous Collecintended to embrace all the octavo publications of the In-. ", IS. stitution,. except the Annual Report.. Its. scope. is. not limited, and. the volumes thus far issued relate to nearly every branch of science. Among these various subjects zoology, bibliography, geology, mineralogy, anthropology,. The. and astrophysics have predominated.. Institution also publishes a quarto series entitled "Smith-. It consists of memoirs based have resulted in imporwhich on extended original investigations,. sonian Contributions to Knowledge". tant additions to knowledge.. C. G. Abbot, Secretary of the Smithsonian Institution.. (. Hi.



CONTENTS Smithsonian Meteorological Tables. (Corrected to January, 193 1.) (Whole volume.). Fifth Revised Edition. 282 pages. 193 1. (Publ.. 3116.). (v).







COLLECTIONS SMITHSONIAN MISCELLANEOUS VOLUME. 86. (WHOLE VOLUME). SMITHSONIAN. METEOROLOGICAL TABLES METEOROLOGICAL AND PHYSICAL TABLES] [BASED ON GUVOT'S. FIFTH REVISED EDITION (Corrected to January, 1931). (Publication 3116). CITY OF WASHINGTON INSTITUTION THE SMITHSONIAN BY PUBLISHED 1931.

The Lord Baltimore. I'ress. Baltimore, Md. printed in the u.s.a..

ADVERTISEMENT TO FIFTH REMSED EDITION. The original edition of. the Smithsonian Meteorological Tables was issued and revised editions were published in 1896, 1897. 1907, and 1918. A fifth revised edition is here presented, which has been prepared under the direction of Charles F. Mar\dn, Chief of the U. S. Weather Bureau, assisted by Herbert H. Kimball, Senior ^Meteorologist of the same bureau. Officials of the U. S. Bureau of Standards have been consulted relative to the value of in 1893,. certain physical constants that enter into the calculation of the tables.. All. errata thus far detected in the earlier editions have been corrected.. The. great development in the exploration of the free air to the height. of the tropopause and even beyond calls for an extension of. some. tables to. adapt them to the low temperatures and pressures experienced at these great heights, and also for a distinction between the symbols for the acceleration of gravity at the surface of the earth and in the free air. Also, the measurement of heights as " geopotentials " in " dynamic meters " calls for five new tables.. The table of international meteorological symbols has been revised, table of " International code for horizontal visibilit}' " has been added. of the. work of extension of. and a. Much. and the computation of new ones has been done by the Aerological Division of the Weather Bureau.. The complete. old tables. revision of the " List of meteorological stations," including. an alphabetical arrangement by continents, countries, and stations, has been effected by Mr. W. \Y. Reed of the Climatological Division, U. S. Weather Bureau.. Charles G. Abbot, Secretary.. Smtthsoniax Institution, March 21, igsi..

ADVERTISEMENT TO FOURTH REVISED EDITION. The. was and revised editions were published in 1896, 1897, and 1907. A fourth revised edition is here presented, which has been prepared under the direction of Professor Charles F. Marvin, Chief of the U.S. Weather Bureau, assisted by Professor Herbert H. Kimball. They have had at their disposal numerous notes left by the late Professor Cleveland Abbe, and have consulted with officials of the U.S. Bureau of Standards and of other Government bureaus relative to the value of certain physical constants that have entered into the calculation of the tables. All errata thus far detected in the earlier editions have here been corrected. New vapor pressure tables, derived from the latest experimental values by means of a modification of Van der Waals interpolation formula devised by Professor Marvin, have been introduced. The table of relative acceleration of gravity at different latitudes has been recomputed from a new equation based upon the latest investigations of the U.S. Coast and Geodetic Survey. These values have been employed in reducing barometric readings to the standard value of gravity adopted by the International Bureau of Weights and Measures, supplementing a table that has been introduced for directly reducing barometer readings from the value of gravoriginal edition of the Smithsonian Meteorological Tables. issued in 1893,. ity at the place of observation to its standard value.. The new. values of vapor pressure and of gravity acceleration thus. obtained, together with a recent and. more accurate determination. of the. density of mercury, have called for an extensive revision of numerous other. and especially of those for the reduction of psychrometric observaand the barometrical tables. Among the new tables added are those for converting barometric inches and barometric millimeters into millibars, for determining heights from pressures expressed in dynamic units, tables of gradient winds, and tables giving the duration of astronomical and civil twilight, and the transtables, tions,. mission percentages of radiation through moist. The. sification, of. tion,. air.. tables of International Meteorological Symbols, of. Cloud Clas-. the Beaufort Scale of Winds, of the Beaufort Weather Nota-. and the List of Meteorological Stations, are among those extensively. revised.. Tables for reducing barometric readings to sea. level,. and. tables of. logarithms of numbers, of natural sines and cosines, of tangents and cotangents,. and. for dividing. by. 28, 29,. and. 31,. with a few others, have been. omitted from this edition. This reprint is from the electroplates that were employed in printing the Fourth Revised Edition, after making certain minor corrections.. Charles D. Walcott, Secretary.. Smithsonian Institution, June, 1924.. iv.

ADVERTISEMENT TO THIRD REVISED EDITION The. original edition of. Smithsonian Meteorological Tables was issued. and revised editions were published. in 1893,. revised edition. is. of the late Professor Langley. McAdie, Charles. in. 1896 and 1897.. A. third. here presented, which has been prepared at the request. F. Marvin,. by the cooperation. of Professors. Alexander. and Cleveland Abbe.. All errata thus far detected have been corrected upon the plates, the. Marvin vapor tensions over. ice. have been introduced,. Professor F.. H.. Bigelow's System of Notation and Formulae has been added, the List of Meteorological Stations has been revised, and the International Meteorological. Symbols, together with the Beaufort Notation, are given. at. the. close of the volume.. R.. Rathbun, Acting Secretary.. Smithsonian Institution, December, 1906.. ADVERTISEMENT TO SECOND REVISED EDITION. The. edition of the Smithsonian Meteorological Tables issued in. 1893. having become exhausted, a careful examination of the work has been made,. my. by Mr. Alexander McAdie, of the United States Weather Bureau, and a revised edition was published in 1896, with corrections upon the plates and a few slight changes. The International Meteorologi-. at. request,. cal. Symbols and an Index were. to. The demand for the work has been so great that print a new edition of the revised work, which is. also added. it. becomes necessary. here presented with. corrections to date. S. P.. Langley, Secretary.. Smithsonian Institution,. Washington City, October 30, 1897..



PREFACE TO EDITION OF. I89^. In connection with the system of meteorological observations estab-. by. lished. Smithsonian. the. meteorological. Miscella neons. so. in. later,. a. 1857,. the. at. volume of the. second. by the author, and. was published. edition. the various series of. after. were. tables. enlarged as to extend the work from 212 to over 600 pages.. In. 1859. third. a. was published, with further amendments.. edition. Although designed primarily ing to the Smithsonian. Europe and After. pages,. Dr.. Institution, the. tables. obtained a. much wider. United States.. the. in. twenty-five. years of valuable service,. by the author. revised. for the meteorological observers report-. and were extensively used by meteorologists and physicists. circulation, in. oi. Collediojis.. years. revision. careful. GuyoT,. as a. in 1852. collection. a. 1850,. by Dr. Arnoi^d. compiled. Henry, and published. request of Secretary. Five. was. tables. about. Institution. was published. GuYOT. died,. and. the. fourth. Before. 1884.. containing over 700. edition,. the. finishing. few tables,. la.st. and the completion of the work was. Wm.. assistant. Prof.. ;. in. work was again. the. intrusted to his. Libbey, Jr., who executed the duties of. final editor.. In a few years the demand for the tables exhausted the edition,. and thereupon. it. appeared desirable to recast entirely the work.. new. After. very. careful. consideration,. three. parts:. Meteorological Tables, Geographical Tables, and. I. decided. to. publish. Physical Tables, each representative of the field,. and independent of the others. geneous. is. latest. tables. knowledge. in. in. its. but the three forming a homo-. series.. Although thus. work. ;. the. so. historically related to Dr.. substantially. changed with. ment, and presentation that. but essentially a. new. it. is. not a. publication. vii. Guyot's Tables, the present. respect fifth. to. material,. arrange-. edition of the older tables,.

PREFACE.. VIU. In. the advantage of. preparation. its. conformity with the recently. issued International Meteorological Tables has been kept steadily in view,. and so. constants. the relation of the. is. sionally adopted. The most important difference in yard to the metre. The value provi-. been. by the Bureau of Weights and Measures of the United. and Geodetic Survey,. States Coast. has. with other decisions, the constants and methods. far as consistent. employed have been followed.. there. used. metre. here. in. the. conversion-tables. and. in. the. transformation of. measures,. linear. =. I. 39.3700 inches,. and. metric. of all. formulae. English involving. such conversions.. A from. number of. large. the International. are credited. To a large. Wm.. amount of. attention. the meteorological. Tables,. when. constants,. other. those taken. ;. sources. official. given to the present work.. to. for. Prof. lyiBBEY. revision, involving considerable recomputation,. tables. contained. was determined. it. and. and. Libbey, Jr., especial acknowledgments are due. had already completed a of. newly computed. Tables. the introduction.. in. Prof.. tables ha\re been. Meteorological. to. the last edition of. in. new. adopt. values for. Guyot's. many. of the. set with new type. This new computation, which was placed under Mr. George E. Curtis, who has also written the. have the present volume. involved a large amount of the. direction. text,. of. and has carefully prepared the whole manuscript and carried. through the press.. To Mr.. Curtis' s interest,. ence as a meteorologist, the present volume Prof.. and. 90,. LiBBEY has contributed Tables. to his special experi-. therefore largely due.. is. 38, 39, 55, 56, 61, 74, 77, 89,. and has also read the proof-sheets of the entire work.. I desire to for. and. express. mj--. acknowledgments. to. Prof. Cleveland Abbe,. the manuscript of Tables 32, 81, 82, 83, 84, 85, 86;. Hazen,. it. for. to. Mr. H. A.. Tables 49, 50, 94, 95, 96, which have been taken from his. Ha7id-book of Meteorological Tables ; the United States Coast and. and also. to. the Superintendent. of. Geodetic Survey, the Chief Signal Officer. of the Army, and the Chief of the Weather Bureau, for. much. valuable. counsel during the progress of the work. S.. P.. LANGIvEY, SecreiaTy..

Table of Contents. PaGE. INTRODUCTION.. xv. Description and use of the Tables. to Ixxxvi. THERMOMETRICAL TABLES.. ^. Conversion of thennometric scales— 1. Approximate Absolute, Centigrade, Fahrenheit, and Reau-. 2. Fahrenheit scale to Centigrade. 5. 3. Centigrade scale to Fahrenheit. 10. 4. Centigrade scale to Fahrenheit, near the boiling point of water. 13. 5 6. Differences Fahrenheit to differences Centigrade. .... ..... 13. mur. 2. scales. Differences Centigrade to differences Fahrenheit. 13. Correction for the temperature of the emergent mercurial column of thermometers. 7. Correction for Fahrenheit thermometers. 14. 8. Correction for Centigrade thermometers. 14. CONVERSIONS INVOLVING LINEAR MEASURES. 16. 9. Inches into millimeters. 10. Millimeters into inches. 23. 11. 36. 12. Barometric inches (mercury) into millibars Barometric millimeters (mercury) into millibars. 13. Feet into meters. 14. Meters into. 40 42. 15. Miles into kilometers. 16. Kilometers into miles. feet. 17. Interconversion of nautical and statute miles. 18. Continental measures of length with their metric and English equivalents. 38. 44 46 48 48. CONVERSION OF MEASURES OF TIME AND ANGLE. 19 20 21. 22 23. Arc into time Time into arc Days into decimals. of a year and angle Hours, minutes and seconds into decimals of a day Decimals of a day into hours, minutes and seconds. 5^ 5^. ^2. 56. 56.

—. ——. table of contents.. x. Page. Table 25. Minutes and seconds into decimals of an hour Local mean time at apparent noon. 26. Sidereal time into. 27. Mean. 24. 57. solar time. 57 58. solar time into sidereal time. 58. mean. CONVERSION OF MEASURES OF WEIGHT. 28. Conversion of avoirdupois pounds and ounces into kilograms. 29. Conversion of kilograms into avoirdupois pounds and ounces. 30. Conversion of grains into grams. 61. 31. Conversion of grams into grains. 62. WIND. .. .. .. .. 60 61. TABLES.. 32. Synoptic conversion of velocities. 64. 33. Miles per hour into feet per second. 65. 34. Feet per second into miles per hour. 65. 35. Meters per second into miles per hour. 66. 36. Miles per hour into meters per second. 37 38. Meters per second into kilometers per hour Kilometers per hour into meters per second. 67 68. 39. Scale of velocity equivalents of the so-called Beaufort scale of. 69. wind Radius of. critical. 70 curvature and velocities of gradient winds for. frictionless. motion. in. highs and lows. —. 40. English measures. 71. 41. Metric measures. 72. REDUCTION OF TEMPERATURE TO SEA LEVEL. 42. English measures. 76. 43. Metric measures. y'j. REDUCTION OF BAROMETER READINGS TO STANDARD UNITS.. 44 45. Reduction of the barometer English measures. to. standard temperature. 80. Metric measures. 100. Reduction of the mercurial column to standard temperature.. (For U-shaped manometers with brass. scales.). —. 46. English measures. 123. 47. Metric measures. 125. Reduction of mercurial barometer to standard gravity. 48. Direct reduction from local to standard gravity. 127. Reduction through variation with latitude 49 50. English measures. 128. Metric measures. 130.

TABLE OF CONTENTS.. 'p^gLE. XI. TABLES FOR DETERMINING HEIGHTS AND CONVERSIONS INVOLVING GEOPOTENTIAL.. Determination of heights by the barometer.. + 0.0010195x36]. PacF. EngHsh measures.. -——. ..... 51. Values of 60368. 52. Term. 53. Correction for gravity and weight of mercury. 139. 54. Correction for an average degree of humidity. 141. 55. Correction for the variation of gravity with aUitude. [1. log.. D. for temperature. i^-?. 137. Determination of heights by the barometer.. .. .. .. 142. Metric and dynamic. measures. 56. Vahies of 18400 log. ^—^. 143. 57. Values of 18400 log. —^^. 144. 58. Temperature correction factor (a = .00367^). 59 60. Temperature correction (o.oo367^xZ). 147. Correction for humidity. 148. 61. Correction for humidity. Auxiliary to Table 58. 150. 62. Correction for gravity and weight of mercury. 63. Correction for the variation of gravity with altitude. 146. 152 .. .. .. 64. Heights reduced from meters to dynamic meters,. 65. Corrections to Table 64 for values of the acceleration of gravity. of gravity at sea level being 9.80. at sea level different. 154. from 9.80. 155. .... 66. Normal. 67. Heights reduced from dynamic meters to geometric meters, the. 68. Corrections to Table dj for values of the acceleration of gravity. 69. Difference of height corresponding to a change of o.i inch in the. value of the acceleration of gravity at sea level. acceleration of gravity at sea level being 9.80. at sea level different. barometer.. 70. •. ..... from 9.80. the barometer.. 155. 156. 157. English measures. Difference of height corresponding to a change of. 153. the- acceleration. 158 i. millimeter in. Metric measures. 159. Determination of heights by the barometer 71. Formula of Babinet. 160. Barometric pressures corresponding to the temperature of the boiling point of water. 72. English measures. 161. 73. Metric measures. 161.

— ——. — Xll. TABLE OF CONTENTS.. rp. HYGROMETRICAL TABLES.. PaGE. English measures. 74. Pressure of aqueous vapor over. ice.. 75. Pressure of aqueous vapor over. w^ater.. 76. Pressure of aqueous vapor over. 77 78. Pressure of aqueous vapor over water. Metric measures. 79 80. Pressure of. 81. ice.. 83. .. .. .. English measures. Metric measures. 169. 170 173. ice.. 175. Weight of a cubic foot of saturated vapor. English measures Weight of a cubic meter of saturated vapor. Metric measures. Values of. e. = e' -o.oooT^GyBit-t'). 176 177. English measures f. 1+. ~^^ \. ..... Temperatures Eahrenheit. Relative Humidity.. 164 i65. .. Dynamic measures aqueous vapor over water. Dynamic measures. Pressure of aqueous vapor over. Reduction of psychrometric observations. 82. .. 180 191. Reduction of Psychrometric Observations. Metric measures 84. Values of ^ = £?' — o.ooo66o5(/; — ^') (i +0.00115^'). 85. Relative humidity.. 86. ..... 194. 200. Temperature Centigrade. Rate of decrease of vapor pressure with altitude for mountain 202. stations. Reduction of snowfall measurements 87 88. Depth of water corresponding to the weight of a cylindrical snow core 2.655 ii^ches in diameter Depth of water corresponding to the weight of snow (or rain). 89. collected in an 8-inch gage. 202 203. Quantity of rainfall corresponding to given depths. 203. GEODETICAL TABLES. 90. Value of gravity on the earth. 91. Relative acceleration of gravity at different latitudes. 92. 93. Length of one degree of the meridian at different latitudes Length of one degree of the parallel at different latitudes. 94. Duration of sunshine. 95. Declination of the sun for the year 1899, at Greenwich apparent. 96. Duration of astronomical twilight. 223. 97. Duration of. 224. 206. at sea level. .... .. .. .. .. .. .. 207 209 210 211. at different latitudes. noon. 222 civil twilight. Relative intensity of solar radiation at different latitudes. 98. Mean. intensity for. 24 hours of solar radiation on a hori-. zontal surface at the top of the atmosphere. 225. 99. Relative amounts of solar radiation received on a horizontal. surface during the year at different latitudes Air mass, m, corresponding to different zenith distances of the sun. 226. 100 loi. Relative illumination intensities. 226. ..... 226.

TABLE OF CONTENTS.. Xlll. MISCELLANEOUS TABLES.. •p^gLg. PacE. 109. Weight in grams of one cubic centimeter of air. English measures Temperature term Humidity term, auxiliary to Table 104 Humidity and pressure terms combined Weight in grams of one cubic centimeter of air. Metric measures Temperature term Humidity term. Auxiliary to Table 107 Humidity and pressure terms combined Atmospheric water-vapor lines in the visible spectrum Atmospheric water-vapor bands in the infra-red spectrum. no. Transmission percentages of radiation through moist. 111. Energy. 112. International meteorological symbols. 241. 113. International cloud classification. 243. 114. Beaufort weather notation. 245. 115. International code for horizontal visibility. 246. 116. List of meteorological stations. 247. Index. 279. 102. 103. 104 105. 106 107. 108. 228. 229 230 232. ..... distribution. and atmospheric transmission of. ation. air. .. .. .. .. .. .. 233 234 237 238. 239. solar radi-. 240.



INTRODUCTION. DESCRIPTION AND USE OF TABLES. THERMOMETRY.. The. present standard for exact thermometry. is the normal centigrade hydrogen thermometer as defined by the International Bureau of Weights and Measures. The constant volume is one liter and the pressure at the freezing point is one meter of mercury reduced to freezing and standard gravity. The scale is completely defined by designating the temperature of melting ice, o°, and of condensing steam, ioo°, both under standard atmospheric pressure. All other thermometric scales that depend upon the physical properties of substances may by definition be made to coincide at the ice point and the boiling point with the normal scale as above defined, but they will diverge more or less from it and from each other at all other points. However, by international consent it is customary in most cases to refer other working scales to the hydrogen. scale of the constant-volume. scale.. The absolute or thermodynamic scale. To obviate the difficulty which thermometers of different type and substance inherently disagree except at the fixed points. Lord Kelvin proposed that temperatures be defined by reference to certain thermodynamic laws. This course furnishes a scale independent of the nature or properties of any particular substance. The resulting scale has been variously named the absolute, the thermodynamic, and, more recently, in honor of its author, the Kelvin scale. The temperature of melting ice by this scale on the centigrade basis is not as yet accurately known, but it is very nearly 273.13, and that of the arises because. boiling point, 373°i3.. Many. problems in physics and meteorology call for the use of the absolute scale; but it is not convenient, and in many cases not necessary, to adhere strictly to the true thermodynamic scale. In fact, the general requirements of science will very largely be met by the use of an approximate absolute scale which for the centigrade system is defined by the equation. T =. (273°. +. t°. C.). quantity, t°, may be referred to the normal hydrogen centigrade scale or be determined by any acceptable thermometric method. This scale differs from the true Kelvin scale, first, because 273° is not the exact value of the ice point on the Kelvin scale, second, because each observed value of t° other than 0° or 100° requires a particular correction to. The observed. XV.

o°.

THERMOMETRICAL TABLES.. XVll. convert i6°9 Centigrade to Approximate Absolute, Fahrenheit, and. To. Reaumur.. From the table, From the proportional. 0.9 16.9. I6°9. Or,. = 289°^.^. = 0.9. = = C.= 289.9 A. A. =. i6? C.. parts. X. 2. (I. - ^) + 32. =. = I2°8 R. = 07 = 13.5 i?.. 6o°8 F. i-6. 62.4 F.. 33-8. - 34 32.0 62.4 F.. convert I47°7 Fahrenheit to Approximate Absolute, Centigrade, and. To. Reaumur. 140° From the table, From the proportional parts 7.7. F.. 147.7 F.. 1477 '. -. 32.0. 333° A. A.. =. 337-3 ^4.^.. 4.3. ^. ^ _^ ^10 ^ J_ 1000 100. (^. 2. = =. ^^^_). = =. 60°. = 64.3. ^. 8. + + +. 578. ,. = =. C.. 4-3. 48° R. 3-4. = 514^-. C.. „. .58. x)6. 64.27 C.. Fahrenheit ing. its. may. also be reduced to. Approximate Absolute by obtain-. equivalent in Centigrade from Table 2 and adding 273 to the result.. To. convert i8°3. Reaumur. Approximate Absolute, Centigrade, and. to. Fahrenheit.. From From. 22.9 C.. = = =. 73.2 F.. 5^ = 22.9 C, and (i8.3X^) + 32 = ^^+ 32. =. 73-2 F.. the proportional parts,. 2.3 T8.3. Or, 18.3. X. ^^. 4. =. = = R. =. 16° R.. the table,. 293° 2.9. 295.9. 4. 4. A.A. = 20°. = A.A. =. C.. 2.9. 68°. 4. TABLE. Table 2.. F.. 5-2. Conversion of readings of the Fahrenheit thermometer. to. 2.. readings. Centigrade.. conversion of Fahrenheit temperatures to Centigrade temperatures The is given for every tenth of a degree from + I30°9 F. to — 120-9 Pthe arguFahrenheit, top and side argument is the whole number of degrees. The. ment, tenths of a degree Fahrenheit. when. desired,. is. hundredths of a degree Centigrade. 2. ;. interpolation to hundredths of a degree,. readily effected mentally.. The. tabular values are given to.

:. .. INTRODUCTION,. XVlll. The formula. for conversion. is. vv^here F° is a given temperature Fahrenheit, and C° the corresponding temperature Centigrade.. Example. To convert 79°7 Fahrenheit to Centigrade. The table gives directly 26°50 C. For conversions of temperatures outside the Table i. Table 3.. Conversion of readings of the Centigrade thermometer Fahrenheit.. The conversion is. limits of the table use. of. readings. to. Centigrade temperatures to Fahrenheit temperatures. + 60.9 to — 90.9 C. tabular values are expressed in hundredths of a degree Fahrenheit.. given for every tenth of a degree Centigrade from. The. The formula. for conversion. is. F° - ^ C°. +. 32°. is a given temperature Centigrade, and F° the corresponding temperature Fahrenheit.. where C°. For conversions of temperatures outside the limits of the Table i or 4. Table 4.. Conversion of readings of the Centigrade boiling point to readings Fahrenheit. This. Example. is. an extension of Table 3 from 90.0. the. to 100.9 Centigrade.. to Fahrenheit.. 9570. C.. 0.04. 9574 5.. near. :. To convert 95°74 Centigrade From the table, By interpolation,. Table. thermometer. table, use. C.. Conversion of differences Fahrenheit. = 204?26 = 0.07 = 204^33. F.. F.. to differences. Centigrade.. The table gives for every tenth of a degree from 0° to 20°9 F. the corresponding lengths of the Centigrade scale..

THERMOMETRICAL TABLES.. XIX TABLE. Table 6.. Conversion of differences Centigrade. to differences. 6.. Fahrenheit.. The table gives for every tenth of a degree from o° to 9.9 C. the corresponding lengths of the Fahrenheit scale. Example:. To. find the equivalent difference in Fahrenheit degrees for a difference. of 4°72 Centigrade.. From From. 4°70 C. =. the table, the table. by moving the decimal point. for 0.2,. 846 = 0.04. 0.02. F.. ^C. ^^F. TABLES. Tables 7,8.. Correction for the temperature of the emergent mercurial. 7, 8.. column. of thermometers.. When. the temperature of the thermometer stem containing a portion. is materially different from that of the bulb, a correcbe applied to the observed reading unless the instrument has been previously graduated for the condition of use. This correction frequently becomes necessary in physical experiments where the bulb only, or else the bulb with a portion of the stem, is immersed in a bath whose temperature is to be determined. In meteorological observations the correction. of the. mercury column. tion needs to. may become. appreciable in wet-bulb, dew-point, and solar-radiation ther-. mometers, when the temperature of the bulb. is. considerably above or below. the air temperature. If ^ be the average temperature of the emergent mercury column, / the observed reading of the thermometer, n the length of the mercury in the '. emergent stem in glass for i°,. in scale degrees,. the correction. an. {t. is. -. and. a the apparent expansion of. mercury. given by the expression t'),ov. -. an {f. -. may. t). be the more convenient form when t is greater than t. with the composition of the glass of which the thermometer stem is composed. For glass of unknown composition the best average value for centigrade temperatures appears to be 0.000155, while for stems of Jena i6^^\ or similar glasses, or Jena 59^^\ the values 0.00016 for the former and 0.000165 for the latter maybe preferred. (Letter from. which. latter. The value. U.S. Bureau of Standards dated January. The use. '. of a varies. 5,. 191 8.). formula given above presupposes that the mean temperature of the emergent column has been determined. This temperature may be approximately obtained in one of three ways, (i) By a " fadenthermoof the. meter" (Buckingham, Bulletin, Bureau of Standards, 8,239, 1911, Scientific Paper 170); (2) by exploring the temperature distribution along the stem and calculating the mean temperature; (3) by suspending along the side of, or attaching to the stem, a single thermometer. If properly placed this.

XX. INTRODUCTION.. thermometer will indicate the temperature of the emergent mercurial column an accuracy sufficient for many purposes. Under conditions ordinarily met with in practice it is desirable to place the bulb of the auxiliary thermometer at some point below the middle of the emergent column. It is to be noted that the correction sought is directly proportional to the value of a, and that this may vary for glass stems of different composition from 0.00015 to 0.000165 for Centigrade temperatures. For thermometers ordinarily used in meteorological work, however, 0.000155 appears to be a good average value for Centigrade temperatures (0.000086 for Fahrenheit temperatures), and the correction formulee, therefore, are, to. T = T = In the above,. T =. — —. t t. 0.000086. 11. (/'. 0.000155 n if. — —. /). Fahrenheit temperatures.. t). Centigrade temperatures.. Corrected temperature.. /. = Observed temperature.. t'. = Mean temperature. of the glass. stem and emergent mer-. cury column.. n. When. t'. \s { (. — Length of mercury. ,. lower. }. than. /. in. the emergent stem in scale degrees.. the numerical correction. is. to. be. ). < (. ,. '. ,. ,. added.. > j. Table 7 gives corrections computed to 001 for Fahrenheit thermometers from the equation C = — 0.000086 « (/' — /). The side argument, n, is given for 10° intervals from 10° to 130°; the top argument, /' — /, for 10° intervals from 10° to 100°. Table 8 gives corrections computed to O.oi for Centigrade thermometers from the equation C = — 0.000155 n (/' — /). The side argument, n, is given for 10° intervals from 10° to 100°; the top argument, /' — /, for 10° intervals from 10° to 80°.. Example:. The observed temperature. of a black-bulb. thermometer. is. 120.4 ^-i. the temperature of the glass stem is 55?2 F., and the length of mercury in the emergent stem is 130° F. To find the corrected temperature. With n= 130° F. and t' — t = — 65° F., as arguments. Table 7 gives the correction o?7 F., to the observed temperature. 121.. I. which by the above rule is to be added The corrected temperature is therefore. F.. CONVERSIONS INVOLVING LINEAR MEASURES.. The fundamental. unit of length is the meter, the length of which is equal between the defining lines on the international prototype meter at the International Bureau of Weights and Measures (near Paris). to the distance. when. this. standard. is. at the temperature of melting ice (0° C).. The. relation.

CONVERSIONS INVOLVING LINEAR MEASURES.. XXI. here adopted between the meter and the yard, the English measure. of. meter = 39.3700 inches, as legalized by Act of U.S. Congress, July 28, 1866. This U.S. Standard of length must be distinguished from the British Imperial yard, comparisons of which with the international prototype meter give the relation i meter == 39-370II3 inches. (See Smithsonian Physical Tables, 1916, p. 7, Table 3.). length,. Table. is. i. Inches into millimeters.. 9.. I. table. = 25.40005. inch. 9.. millimeters.. The argument is given for every hundredth of an inch up to 32.00 inches, and the tabular values are given to hundredths of a millimeter. A table of proportional parts for thousandths of an inch is added on each page. Example. To. :. convert 24.362 inches to millimeters.. The. table gives (p. 20).. +. (24.36. Table 10.. =. .002) inches. (618.75. + O-OS) mm-. 618.80. "=. mm. table. Millimeters into inches.. From O. to. mm.. 400. the argument. is. 10.. given to every millimeter, with. subsidiary interpolation tables for tenths and hundredths of a millimeter. tabular values are given to four decimals. From 400 to looo mm., covering the numerical values which are of frequent use in meteorology for the conversion of barometric readings from the metric to the English. The. barometer, the argument. is. given for every tenth of a millimeter, and the. tabular values to three decimals.. Example. To convert 143.34 mm. The table gives (143. +. .3. +. .04). to inches.. mm. =. (5.6299. +. 0.0118 +0.0016). inches.. inches. = 5.6433. tables. Tables 11, 12.. Conversion. of barometric. readings. into. 11. 12.. standard units oj. pressure.. The equation for the pressure barometric height, B, is. in millibars, ' P„,i,. corresponding to the. 1000. where A ^. is. the densitv of mercury and g^. The value. centimeter, and. of the bar as here defined is. is. the standard value of gravity.. is a pressure of 1,000,000 dynes per square that employed by meteorological services, and recommended by inter-.

^. :. INTRODUCTION.. XXll. In order that pressures thus derived shall be expressed in C.G.S. units is. it. evident that the recognized standard values of the constants of the equa-. tion must be employed. It therefore becomes necessary to abandon the values for the density of mercury and for standard gravity heretofore employed, which had the sanction of the International Meteorological Committee, in favor of the more recently determined values that have been adopted by the International Bureau of Weights and Measures. The value adopted for A is 13.5951 grams per cubic centimeter;^ and for. 980.665 dynes.. (/o,. By. the use of these constants. in. Pmb = 1-333224 B. Pm, =. ^ =. >^3-86395. B. we obtain. and (inches). B. ivhere tion to. Table. 'o^oIIIt. the above equation (millimeters),. is the height of the barometer in the units indicated, after reducstandard temperature and the standard value of gravity.. 1 1. ,. Barometric inches. to. millibars.. The argument is for o.oi inch. From O.OO to 2.49 inches the tabulated values are given to the nearest hundredth of a millibar, so that by removing the decimal one place to the right the value in millibars of every tenth inch. from 0.0 to 24.9 inches. From. may be. obtained to the nearest tenth of a millibar.. 25.00 to 31.99 inches the tabular values are given to the nearest tenth. of a millibar.. The. first. part of the table. may. be used as a table of proportional parts. for interpolation.. Example. To convert 23.86 barometric inches into millibars From Table 11, 23.8 inches = 806.0 millibars " " " " = .06 inch 2.0 = millibars inches 808.0 23.86 Table 12.. Barometric millimeters. The argument. is. to. of pressure.. millibars.. for each millimeter from. I. to 799,. and the tabular. values are given to the nearest tenth of a millibar.. This table. may. also be used to convert millibars into millimeters of. mercury. It is 1,000,000 times greater than Physical Tables, 6th cd., 1914, p. 346. The smaller generally employed by physicists and chemists. See Marvin, Charles F. No-. national meteorological and aerological conferences. that given in. value. is. the Smithsonian. menclature of the Unit of Absolute Pressure. Monthly Weather Review, 1918, 46 73-75. ^ Chappuis, Recueil de Constantes Physiques, Soc. Fr. Phys., 1913, p. 139. Leduc, Trav. et Mem., Bur. Int. Poids et Mes., xvi, p. 36, 1917. * Comptes Rendus des .Seances, Troisieme Conference Generale, p. 68. Trav. et Mem., Bur. Int. Poids et Mes., xii, 1902. :.

CONVERSIONS INVOLVING LINEAR MEASURES. Example. :. To =. XXlll. convert 1003.5 millibars into millimeters of mercury.. (1002.6 +0.9). Table 13.. table. Feet into meters.. From. 1003.5 mb.. mb. = (752 +0.68) mm. = 752.68 mm.. the adopted value of the meter, 39.3700 inches I English foot = 0.3048006 meter.. 13.. —. Table 13 gives the value in meters and thousandths (or millimeters) every foot from o to 99 feet; the value to hundredths of a meter (or centimeters) of every 10 feet from 100 to 4090 feet; and the value to tenths of a meter of every 10 feet from 4000 to 9090 feet. In using the latter part, for. the. first line. Example. of the table serves to interpolate for single feet.. :. To convert 47 feet 7 inches to The table gives By moving the decimal point. meters.. feet. 47 0.583. ". 47.583 feet Table 14.. Meters into. = 47.583 feet. = 14.326 meters. = 0.178 = 14-504 meters.. 47 feet 7 inches. table. feet.. 1. 4.. meter = 39.3700 inches = 3.280833 + feet. 509 meters the argument is given for every unit, and the tabular values to two decimals; from 500 to 5090 the argument is given to every lO meters, and the tabular values to one decimal. The conversion for tenths of a meter is added for convenience of interpolation. I. From o. Example. to. :. Convert 4327 meters to. The. feet.. table gives. +. (4320. Table 15.. 7). meters = (14173.2 +23.0). = 14196.2. Miles into kilometers. mile. I. The. feet. table. = 1.609347. to. 20000 miles. 15.. kilometers.. table extends from o to 1009 miles with. and from looo. feet.. for every. argument. lOOO miles.. The. to single miles,. tabular quanti-. given to the nearest kilometer.. ties are. Table 16.. Kilometers into miles. I. The. table. is.. kilometer = 0.621370 mile.. table extends to 1009 kilometers with. argument. to single kilo-. meters, and from lOOO to 20000 kilometers for every lOOO kilometers. Tabular values are. Example. given to tenths of a mile.. :. Convert 3957 kilometers into miles.. The. table gives. (3000. +. 957) kilometers. =. (1864. i. +. 594.7) miles. =. 2458.8 miles..

:. INTRODUCTION.. XXIV Table. 1. Inter conversion of nautical. 7.. and. statute miles.. The nautical mile as defined by the U.S. Coast and Geodetic Survey (Tables for a polyconic projection of maps. U.S. Coast and Geodetic Sur5, page 4) is "A minute of arc of a great circle a sphere whose surface equals that of the Clarke representative spheroid of 1866," and the value given is 1853.25 meters, or 6080.20 feet.. vey, Special Publication No.. of. Table 18.. Continental measures of length with their metric and English equivalents.. This table gives a miscellaneous alphabetically arranged, with the. and. their metric. list. name. measures of length, country to which they belong. of continental. of the. and English equivalents.. CONVERSION OF MEASURES OF TIME AND ANGLE. Table 19.. Arc. into time.. i=4;i=4,i Example. Change 124°. From. 15'. 24^7 into time.. the table.. = Is 15.

CONVERSION OF MEASURES OF TIME AND ANGLE. additional columns serve to enter the table with the day of the common or the bissextile year as the argument, and be used also for converting the day of the month to the day of the. Two month. may year,. either of the. and. Example. To. vice versa.. :. number. find the. of. days and the decimal of a year between Februin a bissextile year.. ary 12 and August 27. Aug. 27:. Day. Feb. 12:. ". of year ". ". Interval in days. The decimal. = 240; decimal. = j^; = 197;. ". = 0.65435. of a year " ". =0^0499. interval in decimal of. = 0.53936. a year. of the year corresponding to the interval 197 da.ys. may. also be taken from the table by entering with the argument 198.. Table 22.. The Example. 22.. tabular values are given to six decimals. :. Convert. 5*^. 24"" 23^4 to the. decimal of a day: 5^. interpolation, or. by moving the decimal. for 4^. = 0^208333. 24™ =. 016667. = =. 266. 23^. By. table. Hours, minutes and seconds into decimals of a day.. 0.4. 5. 0^225271 Table 23.. Example. Decimals of a day. into hours,. minutes and seconds.. table 23. :. Convert 0^225271 to hours, minutes and seconds: day = 4*^ 48" + 28"' 48^ = 5'' 16™ 48^ 0.22. day = 7"" 12' 0.0052 0.000071 day = 6^05. + +. I7f28. 0.09. = =. 7. 29 28 6.14. 5' 24"^ 23:4. Table 24.. The. Minutes and seconds. into decimals of. an hour.. tabular values are given to six decimals.. Example. Convert. 34"" 28^7 to. decimals of an hour.. 34- =0*^566667 28^. o°7. = =. 7778 194. 0.574639. table 24.

XXVI. INTRODUCTION.. Table 25.. Local. mean. time at apparent noon.. This table gives the local mean time that should be shown by a clock when the center of the sun crosses the meridian, on the 1st, 8th, i6th, and 24th days of each month. The table is useful in correcting a clock by means of a sundial or noon mark. ^. Example. To. :. find the correct local. on December. mean time when. the sun crosses the meridian. 15, 1891.. December 16, 11'^ 56'". By interpolating, it is seen that the change to December 15 would be only one-half minute;. The. table gives for. the correct clock time. is. therefore 4 minutes before 12 o'clock. noon. Table 26.. Sidereal time into. Table 27.. Mean. mean. solar time.. solar time into sidereal time.. According to Newcomb, the length of the tropical year. mean. solar days,'-. Any. is. 365.24220. whence. 365.24220 solar days = 366.24220 sidereal days. mean time may therefore be changed into sidereal time. interval of. by Increasing. it. by. its. —^— ^^. part,. and any. into mean time by diminishing be changed ^ & .7. it. interval of sidereal time. by .r. its. may. —77 part. 366.24220 ^. Table 26 gives the quantities to be subtracted from the hours, minutes and seconds of a sidereal interval to obtain the corresponding mean time interval, and Table 27 gives the quantities to be added to the hours, minutes and seconds of a mean time interval to obtain the corresponding sidereal interval. The correction for seconds is sensibly the same for either a sidereal or a mean time interval and is therefore given but once, thus forming a part of each table. Examples: Change 14'^ 25"^ 36^2 sidereal time into mean solar time. Given sidereal time Correction for 14^. 25" 36!2. Corresponding mean time. =. 14. 23. 14.4.

CONVERSION OF MEASURES OF WEIGHT.. Change 13*^ 37"^ 22!/ mean Given mean time. 2.. XXVll. solar time into sidereal time.. Correction for 13^ 37"". 22!7. Corresponding sidereal time. = = = =. 37"" 22^7. 13''. + + + +. 2™. 8!i3 6.08. 0.06 2. +. 14.27. =. I3. 2. 14.3. 39. 37-0. CONVERSION OF MEASURES OF WEIGHT. TABLE. Table 28.. 28.. Conversion of avoirdupois pounds and ounces into kilograms.. The comparisons of July, 1893, made by the International Bureau of Weights and Measures between the Imperial standard pound and the "kilogram prototype" resulted in the relation: I. pound avoirdupois = 453.592 427. 7. grams.. For the conversion of pounds, Table 28 gives the argument for every tenth of a pound up to 9.9, and the tabular conversion values to ten-thousandths of a kilogram. For the conversion of ounces, the argument is given for every tenth an ounce up to gram.. of. 15.9,. and the tabular values. to. ten-thousandths of a. kilo-. TABLE. Table 29.. From. 29.. Conversion of kilograms into avoirdupois pounds and ounces. the above relation between the I. kilogram =. pound and the kilogram,. 2.204622 avoirdupois pounds. avoirdupois ounces.. = 35.274. The table gives the value to thousandths of a pound of every tenth of a kilogram up to 9.9; the values of tenths of a kilogram in ounces to four decimals; and the values of hundredths of a kilogram in pounds and ounces to three. and two decimals respectively.. Table 30.. Conversion of grains into grams.. Table 31. Conversion of grams into grains.. .. From. I. gram = 15.432356 grains. grain = 0.06479892 gram.. Table 30 gives to ten-thousandths of a for. I. 30, 31.. the above relation between the pound and the kilogram, I. from. tables. to 99,. and. convenience. gram the value of every and hundredths of a. also the conversion of tenths. in interpolating.. grain. grain.

INTRODUCTION.. XXVin. Table 31 gives to hundredths of a grain the vakie of every tenth of a gram from O.I to 9.9, and the value of every gram from i to 99. The vakies of hundredths and thousandths of a gram are added as an aid to interpolation.. WIND TABLES. CONVERSION OF VELOCITIES. Table 32. Synoptic conversion of velocities. This table,^ contained on a single page, converts miles per hour into meters per second, feet per second and kilometers per hour. The argument, miles per hour, is given for every half unit from o to 78. Tabular values are given to one decimal. cision. is. For the rapid interconversion of velocities, when extreme premarked convenience and utility.. not required, this table has proved of. Table 33. Conversion of miles per hour into feet per second. The argument is given for every unit up to 149 and the tabular values are given to one decimal.. Table 34. Conversion of feet per second into miles per hour. The argument is given for every unit up to 199 and the tabular values are given to one decimal.. Table 35. Conversion of jneters per second into miles per hour. The argument is given for every tenth of a meter per second up meters per second, and the tabular values are given to one decimal.. to. 60. Table 36. Conversion of miles per hour into meters per second. The argument is given for every unit up to 149, and the tabular values are given to two decimals. Table 37. Conversion of meters per second into kilometers per hour. The argument is given for every tenth of a meter per second up meters per second, and the tabular values are given to one decimal.. to. 60. Table 38. Conversion of kilometers per hour into meters per second. The argument is given for every unit up to 200, and the tabular values are given to two decimals.. Table 39. Scale of velocity equivalents of the. The. so-called Beaufort scale of wind.. personal observation of the estimated force of the wind on an arbi-. trary scale. is. a method that belongs to the simplest meteorological records and. widely practiced. Although anemometers are used at meteorological observatories, the majority of observers are still dependent upon estimates based. is. largely. upon. that for. their ow^n. many purposes. judgment, and so reliable can such estimates be made they abundantly answer the needs of meteorology as. well as of climatology.. A. great variety of such arbitrary scales have been adopted by dififerent. observers, but the one that has 1. From Hand-Book. come. into the. of Meteorological Tables.. most general use and received. By H.. A. Hazen.. Washington, 1888..

WIND the greatest definiteness of application. TABLES. is. XXIX. the duodecimal scale introduced into. the British navy by Admiral Beaufort about 1800. is taken from the Observer's Handbook of the Meteorological London, edition of 191 7, and the Marine Observer's Handbook of. Table 39 Office,. Meteorology, edition of 1930.. The. velocity equivalents in meters per second. and miles per hour are based on extensive observational data collected by Dr. G. C. Simpson and first published by the Meteorological Office in 1906. Several other sets of ecjuivalents have been published in different countries. For a history of this subject see " Rept. loth Aleeting International Meteorological Committee," Rome, 1913, Appendix VII (London, 1914), and a paper by G. C. Simpson on " The velocity equivalents of the Beaufort scale," Professional Notes No. 44, Air Ministry, ^Meteorological Office, London, 1926.. Simpson points out. many. that the Beaufort scale has been used. by. sailors for. generations to describe the effect of the air in motion on ships and their. and upon the sea. With change in the rig of ships there still remains wind upon the surface of the sea, and to this has been added the effect upon objects on land. Finally, it became desirable to interpret wind force on the Beaufort scale in terms of wind velocity as measured by the anemometer. For this purpose experiments with the anemometer both on land and on sea were made. The results showed considerable discrepancies in the velocity equivalents of winds indicated by different numbers on the Beaufort scale, but Simpson attributes these discrepancies to differences in anemometer exposures during the tests. For example, the Meteorological Office equivalents represent velocities mearigging,. the effect of. sured by an anemometer not. less. than 10 meters above the ground. level,. while. the Deutsche Seewarte equivalents represent velocities measured by ane-. mometers as ordinarily exposed. Simpson proposed a scale of equivalents about midway between those determined by the Meteorological Office and by the Seewarte, respectively, and this compromise scale was adopted by the Commission for Synoptic. Weather Information. of the International Meteorological Organization at. Zurich in 1926, with the proviso that the velocity equivalents correspond on land with the wind speed at a height of approximately 6 meters above a level surface. Since, however, the International Commission for Air its. meeting. in. Navigation has taken as the surface wind that measured at a height of 10 to 15 meters above the ground, it has seemed best in these tables to continue to adhere to the British Meteorological Office equivalents,. which are based. on the equation F = 0.836 V5^, where B is the Beaufort number representing the wind force, and V is the velocity equivalent in meters per second. The velocity equivalents adopted by the Commission for Synoptic Weather Information, referred to above, expressed in statute miles per hour, correspond very closely to the values in Table 39 expressed in nautical miles (knots) per hour..

:. XXX. INTRODUCTION. In the Quarterly Journal of the Royal Meteorological Society, volume. XXX, No. 132, October, 1904, Prof. A. Lawrence Rotch has described an instrument for obtaining the true direction and velocity of the wind at sea aboard a moving. vessel.. If. AB. a line. represents the wind due to the motion. A C the direction of the wind relashown by the drift of its smoke, then, by measuring the the true wind makes with the vessel which is easily done. of a steamer in an opposite direction, and tive to the vessel as. angle. DBA that. by watching the w^ave. B. approach. crests as they. This represents,. C, of the triangle.. it. —we. in direction. —. obtain the third side,. and also. in length,. on the wind. scale used in setting off the speed of the ship, the true direction of the relative to the vessel. wind. and. also. its. true velocity.. direction coincides with the ship's course. the angle between. them. is. The method fails when the and becomes inaccurate when. small.. GRADIENT WINDS.. When the motions of the atmosphere attain a state of complete equilibrium of flow under definite systems of pressure gradients, the winds blow across the isobars at small angles of inclination depending upon the retarding effects of friction.. At. the surface of the earth friction. the angle across the isobars. is. often great.. In the free. is. considerable and. air,. however, the. and for some purposes may be disregarded entirely. Under an assumption of complete equilibrium of motion and f rictionless flow the winds will blow exactly parallel to the isobars that is, perpendicular to the gradient which produces and sustains the motion. Such winds are called gradient winds. The anomalous condition of flow of terrestrial winds perpendicular to the moving force is the result of the modifications of atmospheric motions due to the deflective influence of the earth's rotation, and to that other influence due to the inertia reaction of matter when it is constrained to move in a curved path, and commonly called centrifugal force. The equations for gradient wind motions have long been known to meteorologists from the work of Ferrel and others, and may be written in the following form For Cyclones friction is small,. —. F=. r. V. co2. r\. CO. sin. sin2. (p. +. -. CO. sin. (I). </). For Anticyclones. V= In C. G. S. Units, second;. r= radius. of. (^. — 'V \. F = velocity. AP '•^^. sin-. (.2). </>. pr J. of the gradient. wind. AP = pressure. p=. density of air. gradient in dynes per square centimeter per centimeter; in. in centimeters per. curvature of isobars in centimeters;. grams per cubic centimeter; w = angular. velocity of the earth's rotation.

WIND 2. =. per second. TABLES.. XXXI. IT ,. =. and. In the Northern Hemisphere the. latitude.. 86164. winds gyrate counterclockwise in cyclones and clockwise These gyrations are in the reversed direction each to each Hemisphere. In equation (2) the values of. than. 0)-. sm-. The. (j).. equality. V are. AP =. imaginary. aj=sin-0, or. maximum. in. anticyclones.. value Vc. =. When. =. Vi. V^. (V2 —. i). :. and. same curvature = 0.414 V^. in. .. Winds cannot this isobar the. For the same gra-. 4>. a cyclone the gradient. the isobars are parallel straight lines, a condition very often closely = co and the gradient winds have the value given by. realized in nature, r. either (i) or (2) after squaring, namely,. Vr =. .. V.. For practical units equation. V V==. For. AP. dient and for an isobar with the is. greater. defines. r. pco sin. velocity. —. AP. pco-sin^0. an isobar with minimum curvature. its. Southern. pr. AP. flow parallel to the isobars within this critical isobar.. gradient wind has. in the. for values of. pr fixes. in anticyclones.. R. V. •0053]. =. AP 2 pco sm<^. (i). becomes. If^'^. 2.

INTRODUCTION.. xxxu. Units of Also. pressure.. 13713 pd sin pd sin. (VII) (Millibars) pf/sin^0. and. (V). Rr.. 25-073. =. pc^. 4>. 64552 Radius. (IV). (j). 1.8284. =. F,. 18.806. (VIII) (Millimeters). sin-. 24-5QO _ pd sm^({>. (VI). and. of critical curvature. (IX) (Inches). velocities of gradient. winds for frictionless. motion in Highs and Lows.. Table 40.. English Measures.. Table 41. Metric Measures.. .. tables 40, 41.. These tables give the radius of curvature computed from the equation. of the critical isobar in anti-. cyclones,. pco. ". sm^. the velocity of the wind on this isobar, computed from the equation. pco. the velocity of the. wind on a straight V.. =. sm. (f). computed from the equation. isobar,. AP 2 pco. sm. =. -. 2. </). V. and. the velocity of the wind in a cyclone having the. and on an isobar having a radius puted from the equation cyclone,. Fi. = V, (\/^ -. i). same gradient as the. anti-. of curvature equal to R^,. com-. - 0.414. V,. Table 40, English measures, gives values of R^, in miles, and of F^ Vs, and V Low, in miles per hour. The side argument is the latitude for 10°, and at 5° intervals from 20° to 90°, inclusive. The top argument, d, is the perpendicular distance in miles between isobars drawn for pressure. High,. intervals of. ^. inch.. For values of d one tenth as great as given. in the. 10. heading of the table the values of Re, Vc High,. F^,. and. F Low. are increased. tenfold.. Table 41, metric measures, gives values of Re in kilometers, and of and V Low, in meters per second. The side argument is the same as in Table 40. The top argument, d, is the perpendicular distance. Vc High, Vs, in. kilometers between isobars drawn for pressure intervals of. For values. i. millimeter.. d one tenth as great as given in the heading of the table the values of Re, Vc High, Vs, and F Low are increased tenfold. of.

TEMPERATURE TABLES.. XXXIU. TEMPERATURE TABLES. REDUCTION OF TEMPERATURE TO SEA LEVEL. Table 42. English Measures. Table 43.. Metric Measures.. and for different uniform rates amount in hundredths of a degree Fahrenheit and Centigrade, which must be added to observed temperatures in order to reduce them to sea level. The rate of decrease of temperature with altitude varies from one region to another, and in the same region varies according to the season and These tables give. for different altitudes. of decrease of temperature with altitude, the. the meteorological conditions; being in general greater in. than. in cold ones, greater in. of falling pressure. than. summer than. in areas of rising. warm. latitudes. and greater in areas pressure. For continental plateau in winter,. becomes fictitious or illusory. The use of the and judgment in selecting the rate of decrease of temperature to be used. Much experimental work is now in progress with kites and balloons to determine average vertical gradients. It must be remembered that the tables here given are not tables giving the regions, the reduction often. tables therefore requires experience. data as recently determined for various elevations.. The. tables are given in order to facilitate the reduction of temperature. upward or downward. in special investigations, but the reduction not ordinarily applied to meteorological observations. The tables, 42 and 43, are computed for rates of temperature change ranging from i° Fahrenheit in 200 feet to i° Fahrenheit in 900 feet, and. either is. from. 1°. Centigrade in 100 meters to 1° Centigrade in 500 meters; and for up to 5000 feet and 3000 meters respectively.. altitudes. Example, Table. 42.. Observed temperature at an elevation of 2,500 feet, Reduction to sea le\'el for an assumed decrease in temperature of 1° F. for every 300 feet,. Temperature reduced to sea Example, Table. 52^5 F.. -f. level,. 8°3. 6o°8 F.. 43.. Observed temperature at an elevation of 500 meters, Reduction to sea level for an assumed decrease in temperature of 1° C. for every 200 meters,. Temperature reduced. to sea level,. I2?5 C.. -f. 2?5. i5?o C.. BAROMETRICAL TABLES. REDUCTION TO A STANDARD TEMPERATURE OF OBSERVATIONS MADE WITH MERCURIAL BAROMETERS HAVING BRASS SCALES.. The indicated height of the mercurial column in a barometer varies not only with changes of atmospheric pressure, but also with variations of the temperature of the mercury and of the scale. It is evident therefore that if 3.

XXXIV. INTRODUCTION.. the height of the barometric column is to be a true relative measure of atmospheric pressure, the observed readings must be reduced to the values they would have if the mercury and scale were maintained at a constant standard temperature. This reduction is known as the reduction for temperature, and combines both the correction for the expansion of the mercury and that for the expansion of the scale, on the assumption that the attached thermometer gives the temperature both of the mercury and of the scale. The freezing point is universally adopted as the standard temperature of the mercury, to which all readings are to be reduced. The temperature to which the scale is reduced is the normal or standard temperature of the adopted standard of length. For English scales, which depend upon the English yard, this is 62° Fahrenheit. For metric scales, which depend upon. the meter,. it. is. 0° Centigrade.. As thus reduced, observations made with when con-. English and metric barometers become perfectly comparable. verted by the ordinary tables of linear conversion, viz: inches to millimeters and millimeters to inches (see Tables 9, 10), for these conversions refer to the. meter at 0° Centigrade and the English yard at 62° Fahrenheit.. Prof. C. F.. Marvin. in. the. Monthly Weather Review. pointed out the necessity of caution. in. for July, 1898, has. conversion of metric and English. barometer readings:. Example. :. Attached thermometer, 25.4 C. Barometer reading, 762.15 mm. is converted to Fahrenheit = 77.7 and the reading temperature correction according to table 44 would be 0.133 inch and the reduced reading 29.873. This would be erroneous. The correct conversion is found by taking the correction corresponding to 25^4 C.. If. the temperature. to 30.006 in., the. —. and 762 mm., i.e., — 3.15 mm., which gives a corrected reading of 759 mm., and converted into inches gives 29.882 which is the correct result. Professor Marvin further remarks that circumstances sometimes arise in which a Centigrade thermometer may be used to determine the temperature of an English barometer, or a Fahrenheit attached thermometer may be used with a metric scale. In all such cases the temperature must be brought into the same system of units as the observed scale reading before corrections can be applied, and the observed reading must then be corrected for temperature before any conversion can be made. With aneroid barometers corrections for temperature and instrumental error must be determined for each instrument.. The. general formula for reducing mercurial barometers with brass scales. to the standard temperature. is. r=--R ^. (^ I. -T)-l (t-. +m{t-. T). e) '.

BAROMETRICAL TABLES. in. C =. which. XXXV. Correction for temperature.. B =. Observed height of the barometric column. = Temperature of the attached thermometer. — Standard temperature of the mercury.. /. T. m. — Coefficient of expansion of mercury. = Coefficient of Hnear expansion of brass. — Standard temperature of the scale.. /. 6. The accepted determination of the coefficient of expansion of mercury that given by Broch's reduction of Regnault's experiments, viz:. is. m As a. (for 1° C.). =. io~9. (181792 +0.175/. + 0.035. 1. 16/2).. sufficiently accurate approximation, the intermediate value. m. = 0.0001818. has been adopted uniformly for. all temperatures in conformity with the usage of the International Meteorological Tables. Various specimens of brass scales made of alloys of different com-. show differences in their coefficients of expansion amounting to and sometimes ten per cent, of the total amount. The Smithsonian Tables prepared by Prof. Guyot were computed with the average value. position. eight. /. =. (for 1° C.). 0.0000188; for the sake of uniformity with the International. Meteorological Tables, the value /. the present volume. For. has been used. in. may. in error. easily be. A small. = 0.0000184. by four per. any individual. scale, either. value. cent.. portion of the tables has been independently computed, but the. have been copied from the International Meteoroone inaccuracy having been found and corrected.. larger part of the values logical Tables,. Table 44,. Reduction of the barometer measures.. standard temperature. to. For the English barometer the formula temperature becomes. for reducing. — English. observed readings. to a standard. C=-B m. (tI. in. which. B =. Observed height. 32°). +m. of the. {t. of attached. m. = 0.0001818 X. 9. = o.oooioi. /. = 0.0000184 X. -. = 0.0000102. 9. it. -. 62°). 32°). barometer in English inches. thermometer in degrees Fahrenheit.. = Temperature. t. I. -.

XXXVl. INTRODUCTION.. The combined reduction of the mercury to the freezing point and of the scale to 62° Fahrenheit brings the point of no correction to approximately 28!5 Fahrenheit. For temperatures above 28!5 Fahrenheit, the correction is subtractive, and for temperatures below 28!5 Fahrenheit, the correction. is. by the. additive, as indicated. (+) and (— ) inserted. signs. throughout the table.. The. table gives the corrections for every half degree Fahrenheit from. o° to ioo°.. The. and 31.6. limits of pressure are 19. inches, the corrections. being computed for every half inch from 19 to 24 inches, and for every twotenths of an inch from 24 to 31.6 inches.. Example. :. =. Observed height of barometer Attached thermometer, 54?5 F. Reduction for temperature Barometric reading corrected. for. 29.143. = — =. temperature. 0.068 29.075. TABLE. Table 45.. Reduction. the. of. barometer. to. standard. temperature. 45.. — Metric. measures.. For the metric barometer the formula for reducing observed readings C, becomes. to the standard temperature, 0°. C= -B. ^^ " I. in. which C and. B. +. ^^'. mt. are expressed in millimeters and. /. in. Centigrade degrees.. m. =0.0001818; / =0.0000184. In the table, the limits adopted for the pressure are 440 and 795 millimeters, the intervals being 10 millimeters between 440 and 600 millimeters, and 5 millimeters between 600 and 795 millimeters. The limits adopted for the temperature are 0° and + 35?8, the intervals being o?5 and i-o from 440 to 560 millimeters, and o°2 from 560 to 795 millimeters. For temperatures above 0° Centigrade the correction is negative, and hence is to be subtracted from the observed readings. For temperatures below 0° Centigrade the correction is positive, and from 0° C. down to — 20° C. the numerical values thereof, for ordinary barometric work, do not materially differ from the values for the corresponding temperatures above 0° C. Thus the correction for — 9° C. is numerically the. same. as for -f 9° C.. and. is. taken from the table. In physical work. of extreme precision, the numerical values given for positive temperatures. may be. used for temperatures below. ing corrections:. o'^. C.. by applying. to. them the. follow-.

BAROMETRICAL TABLES.. XXXVll. Corrections to be applied to the tabular values of Table 45 in order to use them zvhcn the temperature of the attached thermometer is below 0° Centigrade..

INTRODUCTION.. XXXVni. Example. :. Observed heights of the mercury in the manometer tubes and -4-375Difference in height of the two cohimns. +6.258. (in.),. 10.633. Attached thermometer, 72 °4 F.. —. Correction for temperature. Manometer reading corrected. for temperature. .042. 10.591. For temperatures above 28? 5 Fahrenheit, the correction is subtractive, and for temperatures below 28^5 Fahrenheit, the correction is additive, as indicated by the signs ( + ) and ( — ) inserted throughout the table. Table 47, Reduction of the mercurial column. in. U-shaped manometers with Metric measures.. brass scales to standard temperature.. an extension of Table 45 to the small differences in height of the mercurial columns as determined with a U-shaped manometer. The values have been obtained from the corrections given in that table by the same process as those given in Table 46 were obtained from Table 44. This table. is. Example Observed heights of the mercury in the manometer tubes (mm.), and —86.7. Dift'erence in height of the two columns :. Attached thermometer, i8?4. + 12 1.5 208.2. C —. Correction for temperature. Manometer reading corrected for temperature For temperatures above 0° C. the correction. 0.6. 207.6. is. negative, and hence. is. to. be subtracted from the observed readings. For negative temperatures see the. explanation of Table 45.. reduction of the mercurial barometer to standard gravity.. Tables 48, 49, 50. The mercurial barometer does not directly measure the atmospheric pressure. The latter is proportional to the weight of the mercurial column, and also to. its. height after certain corrections have been applied.. height of the barometric. column. is. easily. measured, by. common. Since the. consent the. pressures are expressed in terms of this corrected height.. The observed the. height of the barometer changes with the temperature of. mercury as already shown, and. gravity, as well as with the pressure.. also with the variations in the value of. Therefore, to obtain a height that shall. be a true relative measure of the atmospheric pressure, the observed height of the mercurial column. be. if at. must not only be reduced. a standard temperature, but also to what. value of gravity.. what its height would would be at a standard. to it.

BAROMETRICAL TABLES.. As dynes.. Stated on page xxii, the standard valne of gravity adopted. At. the time of. " latitude 45°. Inter, d.. More. is 980.665 adoption this value was assumed to apply for. its. sea-level ". and. Poids. on the basis of the absolute determination of. Bureau by DefTorges, 1887-1890 (Proces-Verbaux,. at the International. g Comite. XXXIX. et. Mesures, 1887, pp. 27-28, 86; 1891,. recent determinations/ based. p. 135).. upon numerous measurements. in all. parts of the world, and assuming a certain ideal figure for the earth, give. for the. mean value. of. ^. at latitude. 45° and sea level the value 980.621. This differs from the standard value by 0.044 dyne.. dynes.. of this magnitude from the. mean. frequently encountered, and in some cases surpassed. to. topography and. isostatic. Departures. sea-level gravity of a given latitude are. They. are attributed. compensation, and to gravity anomalies.. For. example, according to Bowie,- at Pikes Peak, Colo., the correction for. topography and compensation is. -|-. 0.187 dyne, while the gravity anomaly''. dyne, giving a total gravity departure of. -1-0.021. at Seattle,. is. Wash., from the mean of measurements. rection for topography. and compensation. -|-. 0.208 dyne.. Also,. two stations, the cor—0.019 dyne* and the grav-. is. at. —0.093 dyne,^ giving a total gravity departure of — 0.112 dyne. The gravity departure at Pikes Peak is sufficient to cause the baromity. anomaly. is. eter to read 0.004 inch or o.io sufficient to. mm.. low, while the departure at Seattle. cause the barometer to read 0.003 i^^h or 0.09. mm.. compared with what the readings would have been with gravity. is. high, as. at. normal. intensity for the latitudes of the respective stations.. From. the foregoing. it. is. evident that the value of local gravity, gi, at. observing station must be determined before the barometer reading. the. can be accurately reduced to standard gravity. cially at sea,. value ing. may. it. not practicable to measure. is. In. gi.. many. cases,. and espe-. In the United States. its. frequently be determined with sufficient accuracy in the follow-. manner ( 1 ). Compute. from the equation 5^0. (2). g,i,^. mean. gravity at sea level for the latitude of the station,. ^. = 978.039 = 980.621. (1+0.005294 sin- ^ — 0.000007 sin= 2<^), (1—0.002640 cos 2^-1-0.000007 COS^ 2</)). Correct g^ for altitude by the equation^ c. (dynes). c. (dynes). = —0.0003086 h (meters), = —0.000094 h (feet),. or. 1 Investigations of gravity and isostasy, by William Bow^ie. U. S. Coast and Geodetic Survey, Special Publication No. 40, 1917, p. 134. • Op. cit., p. 50. 3 Op. cit., p. 59. 4 Op. cit., p. 50. 5 Op. cit., p. 59.. 6. Bowie, op.. cit.,. p.. 134.. 7. Bowie, op.. cit.,. p. 93..

:. INTRODUCTION.. xl. where. li. is. the akitude of the station above sea level. (/^ for gravity anomaly.^ <70 is to be corrected for topography. (3) Correct (4) Finally, pensation.^. and. isostatic. com-. Example. To. local gravity, gj, at the Weather Bureau Atlanta, Ga., latitude t>2>° 45' N., longitude 84° 23' W., height of barometer above sea level. 1218 feet. From Table 90, mean sea level gravity for lat-. determine the value of Office,. =. itude 33° 45' Correction for height of barometer. 979-631 dynes.. =—. (—0.000094x1218) Correction for gravity anomaly, Correction for topography and compensation Local gravity at Weather Bureau Office, Atlanta, Ga.. " ". 0.1 14 0.023 0.014. =— = -f-. ". = 979-508 dynes. of barometer determined the reduction readings to stanHaving gu dard gravity is easily and accurately accomplished by multiplying by the ratio gi/go, or by applying a correction to the barometer reading, other-. —^—-5.. wise corrected, derived from the expression --^^. With giKQo. the. correction is to be subtracted; with gi'>go the correction is to be added. In general, sufficient accuracy will be attained by computing the gravity correction for a station once in. which Bn is the normal same units as En-. for. station. all. from the equation. C = Bn. barometer pressure, and. C. is. ~. -i!^. expressed. in the. Table 48 gives corrections to reduce barometer readings to standard gravThe top argument is the barometer reading. The side argument is the difference, gi—go, for each tenth of a dyne up to 4.0 dynes. The relation is a linear function of both gi—go and B, and for barometer readings 10 or 100 times greater than those given in the argument the correction may be obtained by removing the decimal point in the tabulated values one or two ity.. The correction obtained will be expressed units as the barometer reading to be corrected.. places, respectively, to the right.. same Example i.. in the. The barometer reading. corrected for temperature. The. local value of gravity is 978.08. From the table,. the correction for a barometer reading of 20 inches the correction for a barometer reading of 9 inches the correction for a barometer reading of 0.65 inches. Correction for a barometer reading of 29.65 inches Corrected barometer reading =29.647 in. —0.078 in. 1. In most cases the gravity anomaly. may. is. 29.647 inches, and the. difference,. gi—go, =—2.585.. = — 0.0527 = — 0.0237 = — 0.0017 = — 0.078 = 29.569. in. in.. ^^• in. in.. be obtained from Bowie's paper, op.. cit.,. figure II. 2. but in. In some cases this correction. many. cases,. for each station.. and especially. may. in. be obtained from Bowie's paper, op.. mountainous. districts,. it. cit.,. pp. 50-52,. must be separately computed.

BAROMETRICAL TABLES. Example. xH. 2.. to 0°. The barometer reading reduced value of gravity the table,. is. The. 981.51.. C. is 637.42 mm., and the local difference, ^z (70= +0.845. From. —. the correction for a barometer reading of 600 the correction for a barometer reading of 30 the correction for a barometer reading of 7. =+ =+ =+ —+. mm. mm. mm.. Correction for a barometer reading of 637.4 i^"'!^''Corrected barometer reading =637.42 + 0.55. 0-5i7 0.026 0.006. "ini.. mm. mm.. <^-55. n\n'i-. =+637.97. mm.. In the case of barometer readings made at sea, and also at some land local gravity with greater acit is not practicable to determine curacy than it can be computed from the equations for variations with latitude and altitude given above. The reduction to standard gravity, accordingly, consists of two parts a correction for altitude, and a correction stations,. —. from the computed. sea-level gravity for the latitude of the station to stan-. dard gravity. The first part of the correction, or the correction for altitude, be computed once for all from the expression c=— 0.0003086 li Bn (metric measures), or c= —0.000094 h Bn (English measures), and is usually combined with the reduction of the barometer to sea level or to some other reference plane. The second part has heretofore consisted of a correction for the difference between the mean value of gravity for the latitude of the station and for latitude 45° and, in accordance with the equation given. may. ;. above,. it. may. be derived from the expression (. where 1. is. (f>. r. —0.002640 cos 2. (^. + 0.000007 cos- 2 (f>)B and B is the barometer. the latitude of the station, ^-. ..1. value of the ratio. ^ =. ffi5'—go. reading.. The. 980.621—980.665 . _, ^ =—0.000045. = ^^ Therefore,. ^. 980.665 go the expression for the gravity correction becomes (. —0.00264 cos 2 ^ + 0.000007. COS" 2. (^. — 0.000045)5. Table 49 (English measures) gives the corrections in thousandths of an inch for every degree of latitude and for each inch of barometric pressure from 19 to 30 inches, to reduce barometer readings to standard gravity, computed from the equation. C=(— 0.00264 cos 2<f> + 0.000007 cos^ 2 — 0.000045 B ). Table 50 (metric measures) gives the same corrections in hundredths of a millimeter for each 20 millimeters barometric pressure from 520 to 780 millimeters.. Example: Barometric reading (corrected for temperature) 63° 55', Correction to standard gravity, Table 49, Barometer reduced to standard gravity,. at latitude. =27434. inches. =0.043 inches =27.477 inches. The adoption of this new value for standard gravity may require a slight correction to old barometric records in order to make the entire series of readings homogeneous. The amount of this correction will be the difference between the gravity correction computed by these new tables and by the old tables..